Exoplanets

Planets beyond the Solar System through orbits, transits, and radial velocities.

Conceptual context

An exoplanet is rarely seen as a resolved world. It is usually inferred from a dynamical or luminous footprint around a star. The central question starts from that footprint: $P$ gives the rhythm of the orbit, while $a$ gives its spatial scale. Together they turn a periodic dimming or a spectral wobble into information about the system. If transits, radial velocities, and thermal estimates are also available, the portrait gains $R_planeta$, $M_planeta_sini$, $T_eq$, and $\rho_{planeta}$. The physical craft is to turn a tiny signal into planetary architecture.

🟢 Essential level

$P$ is the exoplanet clock: it tells how often the planet repeats its motion around the star.

$a$ is the characteristic orbital distance, not just any instantaneous separation. In an orbit dominated by stellar gravity, a more distant planet takes longer to complete one revolution because the path is larger and the average gravitational pull is weaker. Therefore the relation between $P$ and $a$ reveals the scale of the system and, with $M_estrella$, checks whether the observed signal fits a Keplerian orbit. Transits add $\delta$ and $R_planeta$, while radial velocity adds $K$ and $M_planeta_sini$. Thus one periodic signal can become orbital size, geometry, and a clue to the planet nature. The planet is not photographed directly; its orbit writes a faint but measurable clock in the data.

51 Pegasi b, the first exoplanet detected around a Sun-like star, illustrates this well: its $P$ is only 4.2 days and its $a$ is about 0.05 AU, far smaller than the distance between Mercury and the Sun. That extreme closeness revealed the existence of so-called "hot Jupiters", gas giants orbiting tight against their star, a configuration classical planet-formation models did not anticipate.

🔵 Formal level

Basic formulas

The formal core is Kepler third law adapted to a star planet system. With $G$, $M_estrella$, $M_planeta$, $P$, and $a$, it relates the time scale to the spatial scale. In many cases $M_planeta$ is much smaller than $M_estrella$, so the central mass dominates the result.

Kepler third law for an exoplanet

If the exoplanet transits, the relative flux drop is approximated by the ratio of apparent areas. $\delta$ connects $R_planeta$ and $R_estrella$, so the planet size can be estimated when the star is well characterized.

Planetary transit depth

Real student questions

Does a short $P$ always mean a small planet? No. It means a close orbit or a more massive star than expected; size is inferred from $\delta$ and $R_estrella$.

Why does radial velocity give $M_planeta_sini$ and not always $M_planeta$? Because the signal depends on $i$. If the orbit is not edge-on, we see only part of the stellar motion.

Does $T_eq$ say whether there is life? No. It only estimates radiative balance using $T_estrella$, $R_estrella$, $a$, and $A_B$. Atmosphere, clouds, and composition matter.

Is a point off the graph curve an error? It may be data error, wrong $M_estrella$, important $e$, another perturbing planet, or a misidentified signal.

Final synthesis

An exoplanet is revealed by repeated patterns. $P$ and $a$ draw the dynamical spine; transits, radial velocities, temperature, and density add physical flesh to the skeleton.